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Use indirect reasoning in geometry
Worksheet
Grade Level
Geometry
GEO.21 Use indirect reasoning in geometry
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Triangles ΔMNP and ΔRST satisfy MN = 12, NP = 18, RS = 20, ST = 30, and ∠N ≅ ∠S (the included angles between the listed sides). You want to prove the triangles are similar by contradiction. Which assumption and contradiction pair works?
A
Assume the triangles are similar; then claim the side ratios 12:20 and 18:30 are not equal, contradicting arithmetic but starting with the wrong assumption.
B
Assume ∠M ≅ ∠R; then the triangles are similar, which is not enough information.
C
Assume ΔMNP is not similar to ΔRST; but MN:RS = 12:20 and NP:ST = 18:30, and these ratios are equal, with included angle ∠N ≅ ∠S, so SAS similarity forces the triangles to be similar, contradicting the assumption.
D
Assume MP = RT; then the triangles are similar, which is not implied.
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